Abstract
This paper analyses the frequency stability of ac grids in the presence of non-dispatchable generation and stochastic loads. Its main goal is to evaluate conditions in which the system is robust to large, persistent active power disturbances without recurring to time-domain simulations. Considering the ongoing energy transition to more renewable sources, defining robustness boundaries is a key topic for power system planning and operation. However, much of the research on long-term studies has not dealt with robust dynamic constraints, while short-term analyses usually depend on time-consuming simulations to evaluate nonlinearities. To bridge this gap, the authors derive an algebraic equation that provides sufficient conditions for robust frequency stability in ac power systems and a relationship among four key quantities: the maximum active power perturbation, the minimum system damping, the steady-state and the transient frequency limits. To achieve this goal, it uses a nonlinear average-model of the ac grid and Lyapunov's direct method extended by perturbation analysis requiring only limited knowledge of the system parameters. The algebraic calculations are validated using time-domain simulations of the IEEE 39-bus test system and results are compared to the traditional Swing Equation model.
Highlights
A NY modern society requires an energy system that is affordable, accessible, secure and sustainable
The text is organized as follows: section II introduces a nonlinear, average model of the ac grid that is appropriate for frequency stability analysis during large active power disturbances (APDs); section III presents the main proposition of this work followed by its mathematical proof; section IV validates the proposition using time-domain simulations of the IEEE 39-bus test system [26] and compares its results to the linear Swing Equation model; section V discusses applications of the proposition, its main limitations and directions for future research; section VI presents the concluding remarks
By deriving sufficient conditions for robust frequency stability of ac power systems operating under large APDs, it defines an algebraic relationship between four system boundaries: the maximum APD Pb, the minimum equivalent damping coefficient Dmin, the transient rtr and rss steady-state frequency limits
Summary
A NY modern society requires an energy system that is affordable, accessible, secure and sustainable. TDSs provide the most accurate results but are hard to integrate in optimization problems such as optimum power flow, while linearizations around an operation point do not give realistic values for frequency deviations during large active power disturbances (APDs) Taking into account this background, the main contribution of this paper is the derivation of sufficient conditions for frequency stability of an ac power system where sources and loads are subject to non-vanishing, bounded perturbations. The text is organized as follows: section II introduces a nonlinear, average model of the ac grid that is appropriate for frequency stability analysis during large APDs; section III presents the main proposition of this work followed by its mathematical proof; section IV validates the proposition using time-domain simulations of the IEEE 39-bus test system [26] and compares its results to the linear Swing Equation model; section V discusses applications of the proposition, its main limitations and directions for future research; section VI presents the concluding remarks
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